1) Note! - the resistivity depends strongly on the presence of impurities in the material.

2) Note! - the resistivity depends strongly on the temperature of the material. The table above is based on 20oC reference.

The electrical resistance of a wire is greater for a longer wire and less for a wire of larger cross sectional area. The resistance depend on the material of which it is made and can be expressed as:

R = ρ L / A (1)

where

R = resistance (ohm, Ω)

ρ = resistivity coefficient (ohm m, Ω m)

L = length of wire (m)

A = cross sectional area of wire (m2)

The factor in the resistance which takes into account the nature of the material is the resistivity. Since it is temperature dependent, it can be used to calculate the resistance of a wire of given geometry at different temperatures.

The inverse of resistivity is called conductivity and can be expressed as:

σ = 1 / ρ (2)

where

σ = conductivity (1 / Ω m)

Example - Resistance in an Aluminum Cable

Resistance of an aluminum cable with length 10 m and cross sectional area of 3 mm2 can be calculated as

R = (2.65 10-8 Ω m) (10 m) / ((3 mm2) (10-6 m2/mm2))

= 0.09 Ω

Resistance

The electrical resistance of a circuit component or device is defined as the ratio of the voltage applied to the electric current which flows through it:

R = V / I (3)

where

R = resistance (ohm)

V = voltage (V)

I = current (A)

Ohm's Law

If the resistance is constant over a considerable range of voltage, then Ohm's law,

I = V / R (4)

can be used to predict the behavior of the material.

Temperature Coefficient of Resistance

The electrical resistance increases with temperature. An intuitive approach to temperature dependence leads one to expect a fractional change in resistance which is proportional to the temperature change:

dR / Rs = α dT (5)

where

dR = change in resistance (ohm)

Rs = standard resistance according reference tables (ohm)

α = temperature coefficient of resistance

dT = change in temperature (K)

(5) can be modified to:

dR = α dT Rs (5b)

Example - Resistance of a Carbon resistor when changing Temperature

A carbon resistor with resistance 1 kΩ is heated 100 oC. With a temperature coefficient -4.8 x 10-4 (1/oC) the resistance change can be calculated as